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摘要:
本文基于Schupmann消色差理论，介绍了一种离轴四反射镜衍射成像光学系统设计方法。设计了口径1 m、F数为8、视场0.12°、波段582.8 nm~682.8 nm的离轴四反射镜衍射成像光学系统。设计结果表明，该光学系统的色差得到有效校正，系统调制传递函数(MTF)在50 lp/mm范围内优于0.53，弥散斑半径的均方根值小于艾里斑半径，成像质量接近衍射极限。分析了平面衍射物镜和曲面衍射校正镜可分别采用二元光刻工艺和金刚石车削技术制作的原因。对设计结构进行公差分析，确定公差误差主要来源于中继反射镜的倾斜角度，为装调过程提供指导。设计的系统为宽波段、高像质的反射式衍射成像光学系统发展提供了参考。
Abstract:According to the Schupmann's achromatic theory, a calculation method of off-axis four-mirror diffractive imaging optical system is introduced. By using the method, an optical system which has an aperture of 1 m, F-number of 8, full field of view of 0.12°, waveband of 582.8 nm~682.8 nm is designed. The results show that the chromatic aberration is corrected effectively. The modulation transfer function (MTF) is more than 0.53 in the range of 50 lp/mm, and the RMS radius of diffusion spot is less than the airy radius. It demonstrates that the image quality of this system is close to the diffraction limit. It is analyzed that the processing of diffractive primary lens and diffractive correct mirror can be realized by traditional lithography and diamond turning, respectively. Monte-Carlo simulation of tolerance analysis is carried out, it determined that the tolerance error mainly originates from the tilt angle of relay mirror, which provides guidance for the process of assembling and adjusting. This system has the advantages of broadband, high image quality, which can provide references for the development of reflective diffractive imaging optical system.
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Key words:
- optical design /
- diffractvie imaging /
- off-axis /
- four-mirror
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Overview: The most effective way to improve the resolution of space optical telescope is to enlarge the aperture. With the increase of aperture, it has become increasingly difficult for traditional reflective space telescope system considering manufacturing technology, the ability to launch and space expansion as well as adjustment technology. Furthermore, considering the support and control structure, the weight of optical telescope system is proportional to the square of aperture. As a result, the control becomes more complex and the cost of optical system is increasing rapidly. Compared with the reflective telescope optical system, diffractive imaging system based on the thin film material as the objective lens can achieve large diameter, high resolution, light weight structure, space packagable and deployable, loose tolerance and so on. Diffractive imaging technology can save launch and manufacturing costs significantly, and has great potential applications in the field of high orbit high-resolution imaging. The existing eyepiece systems of diffractive telescopes mostly use refractive structure, but it can hardly meet the requirements of large aperture space optical telescope in terms of complexity and quality. The reflective eyepiece system has obvious advantages of high image quality, light weight and wide waveband because of its non-chromatic aberration and deflection of optical path. To realize an off-axis reflective diffractive imaging optical system with broadband and compact structure, we analysis the basic principle of diffractive imaging optical system. According to the Schupmann’s achromatic theory, a calculation method of off-axis four-mirror diffractive imaging optical system is introduced. By using the method, an optical system which has an aperture of 1 m, F-number of 8, waveband of 582.8 nm~682.8 nm and the full field of view of 0.12° is designed. The results show that the chromatic aberration is corrected effectively. The modulation transfer function (MTF) of the full field of view is more than 0.53 in the range of 50 lp/mm, the RMS radius of diffusion spot is less than the airy radius. It demonstrates that the image quality of system is close to the diffraction limit. It is analyzed that the processing of diffractive primary lens and diffractive correct mirror can be realized by traditional lithography and diamond turning, respectively. Monte-Carlo simulation of tolerance analysis is carried out, it determined that the tolerance error mainly originate from the tilt angle of relay mirror, which provides guidance for the process of assembling and adjusting. This system has the advantages of broadband, short optical path, ideal obscuration, which can provide references for the development of reflective diffractive imaging optical system.
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图 3 离轴四反射镜衍射成像光学系统结构
Figure 3. Structure of diffractive imaging optical system based on off-axis four-mirror
图 4 衍射物镜100 nm波段轴向色差
Figure 4. Focal shift of 100 nm wavelength for diffractive primary lens
图 10 衍射物镜的相位和线频率径向分布曲线
Figure 10. Phase and line frequency versus aperture of diffractive primary lens
图 11 衍射校正镜的相位和线频率径向分布曲线
Figure 11. Phase and line frequency versus aperture of diffractive correct mirror
表 1 同轴四反射镜衍射成像光学系统初始结构参量
Table 1. Initial parameters of diffractive imaging optical system based on coaxial four-mirror
Surface Radius/mm Thickness/mm Diffractive objective — 20000.000 Primary mirror -1980.200 -1000.000 Secondary mirror -666.561 1000.000 Tertiary mirror -1004.784 -1000.000 Diffractive correct mirror 100.000 70.000 Image — — 
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表 2 优化后的离轴四反射镜衍射成像光学系统结构参量
Table 2. Optimized parameters of diffractive imaging optical system based on off-axis four-mirror
Surface Radius/mm Thickness/mm Conic Diameter/mm Diffractive objective — 20750.000 — 1000 Primary mirror -9925.477 -1938.785 -2.794 160 Secondary mirror 45520.000 1938.785 -4.982 200 Tertiary mirror 153600.000 -1938.785 2.745 250 Diffractive correct mirror 1539.624 2148.094 -0.160 270 Image — — — 17
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表 3 衍射面多项式系数
Table 3. Coefficient of diffractive surface
Surface Coefficient Diffractive objective -0.248, 1.551E-010, -1.926E-019, -6.008E-027, 1.026E-032 Diffractive correct mirror 3.411, 3.141E-007, -1.094E-013, 1.392E-017, -4.556E-022
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表 4 蒙特卡洛最终分析结果
Table 4. Final Monte-Carlo analysis results
Monte-Carlo analysis MTF value ≥98% 0.111 ≥90% 0.165 ≥80% 0.216 ≥50% 0.302 ≥20% 0.400 ≥10% 0.439 ≥2% 0.481
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表 5 最敏感的公差分析结果
Table 5. Results of the most sensitive tolerance analysis
Type Value Criterion Change TETY 3 4 0.00140000 0.32911857 -0.19965035 TETY 3 4 -0.00140000 0.32911857 -0.19965035 TETX 3 4 0.00140000 0.38914889 -0.13962002 TETX 3 4 -0.00140000 0.39516929 -0.13359962 TEDY 3 4 0.01000000 0.49963567 -0.02913324 TEDY 9 9 -0.01000000 0.50957441 -0.01919451 TEDX 3 4 0.01000000 0.51019057 -0.01857834 TEDX 3 4 -0.01000000 0.51019057 -0.01857834 TEZI 5 -1.5820E-005 0.51396962 -0.01479929 TEDX 9 9 0.01000000 0.51761049 -0.01115843
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